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19 May 2024, 00:32
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
61% (01:19) correct
38% (00:47) wrong based on 13 sessions
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Date
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Which of the following could be the graph of all values of x that satisfy the inequality \(2-5x ≤ - \frac{6x-5}{3}\)
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22 Jun 2024, 02:26
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Official Explanation
To determine which of the graphs is the correct answer, you first need to determine all values of x that satisfy the inequality. To do that you need to simplify the inequality until you isolate x.
You can begin by multiplying both sides of the inequality by 3 to obtain \((3)(2-5x)≤ - (6x-5)\). Note that when you multiply by 3, the right-hand side of the inequality becomes \(-(6x - 5), not -6x - 5\). The rest of the simplification is as follows.
The graphs in the answer choices are number lines on which only the number 0 is indicated. Therefore, you do not need to locate 1/9 on the number line; it is enough to know that 1/9 is a positive number. Choice C is the only choice in which the shaded part of the line is equal to or greater than a positive number. Therefore, the correct answer is Choice C.
Answer: C
To determine which of the graphs is the correct answer, you first need to determine all values of x that satisfy the inequality. To do that you need to simplify the inequality until you isolate x.
You can begin by multiplying both sides of the inequality by 3 to obtain \((3)(2-5x)≤ - (6x-5)\). Note that when you multiply by 3, the right-hand side of the inequality becomes \(-(6x - 5), not -6x - 5\). The rest of the simplification is as follows.
\(=(3)(2-5x)≤ - 6x-5\\
\\
=6-15x≤ - 6x-5\\
\\
=-15x≤ -6x-1\\
\\
=-9x≤ -1\\
\\
=x≥\frac{1}{9}\)
Note that when an inequality is multiplied (or divided) by a negative number, the direction of the inequality reverses.\\
=6-15x≤ - 6x-5\\
\\
=-15x≤ -6x-1\\
\\
=-9x≤ -1\\
\\
=x≥\frac{1}{9}\)
The graphs in the answer choices are number lines on which only the number 0 is indicated. Therefore, you do not need to locate 1/9 on the number line; it is enough to know that 1/9 is a positive number. Choice C is the only choice in which the shaded part of the line is equal to or greater than a positive number. Therefore, the correct answer is Choice C.
Answer: C
